CN113408023B - Corner-based beam and plate vertical displacement calculation method - Google Patents
Corner-based beam and plate vertical displacement calculation method Download PDFInfo
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Abstract
The invention discloses a beam and plate vertical displacement calculation method based on a corner, which comprises the steps of measuring and obtaining a span length l of each span of a bridge or a plate body, an actual measurement inclination angle theta of each span and absolute value ordinate H of span ends of two ends of each span, and calculating to obtain a final positive angle alpha; final correction is carried out on the inclination angles theta of the m spans by using the final positive angle alpha to obtain a final positive inclination angle theta'; constructing a cross-deflection curve function of the bridge or the plate body; constructing an orthogonal polynomial basis function, and fitting a cross deflection curve function of the constructed bridge or plate body by using a least square method of the orthogonal polynomial basis function to obtain a preliminary deflection curve function of the whole bridge or plate body; and carrying out sedimentation final correction on the preliminary deflection curve function of the whole bridge or the plate body to obtain the final deflection curve function of the whole bridge or the plate body. The method has the characteristics of high calculation accuracy and small error, so that the calculated bridge axis longitudinal plane displacement value is more accurate, and the bridge axis longitudinal plane displacement value can be objectively and accurately reflected.
Description
Technical Field
The invention relates to the technical field of monitoring of steel structures, concrete structure plate bodies, beam bodies and bridges, in particular to a beam and plate vertical displacement calculation method based on corners.
Background
Along with the rapid promotion of economic strength in China, the number of concrete structure plates, beam bodies, steel structures and bridge construction is increased year by year, wherein the construction proportion of large and medium-sized bridges is increased year by year. However, accidents such as concrete structure plate bodies, beam bodies, steel structures and bridge damage and even collapse caused by numerous factors such as structural degradation, natural factor damage, external force, environmental mutation and the like are increased year by year. Therefore, the health conditions of the concrete structure plate body, the beam body, the steel structure and the bridge need to be monitored, because the concrete structure plate body, the beam body, the steel structure and the bridge can be settled, the axial longitudinal plane displacement values of the concrete structure plate body, the beam body, the steel structure and the bridge need to be monitored in the process of monitoring the concrete structure plate body, the beam body, the steel structure and the bridge, and the existing axial longitudinal plane displacement value calculation processing method has larger calculation error and can not objectively and accurately reflect the axial longitudinal plane displacement values of the concrete structure plate body, the beam body, the steel structure and the bridge. Therefore, the method improves the method, and provides a beam and plate vertical displacement calculation method based on the rotation angle.
Disclosure of Invention
In order to solve the technical problems, the invention provides the following technical scheme:
the invention discloses a beam and plate vertical displacement calculation method based on a corner, which comprises the following steps:
step S1: measuring to obtain the span length l of each span of the bridge or the plate body, the actually measured inclination angle theta of each span and the absolute value ordinate H of the span ends of the two ends of each span, and calculating to obtain a final positive angle alpha;
step S2: final correction is carried out on the inclination angles theta of the m spans by using the final positive angle alpha, so as to obtain a final positive inclination angle theta' after final correction;
step S3: constructing a cross-deflection curve function of the bridge or the plate body;
step S4: constructing an orthogonal polynomial basis function, and fitting a cross deflection curve function of the constructed bridge or plate body by using a least square method of the orthogonal polynomial basis function to obtain a preliminary deflection curve function of the whole bridge or plate body;
step S5: and carrying out sedimentation final correction on the preliminary deflection curve function of the whole bridge or the plate body to obtain the final deflection curve function of the whole bridge or the plate body.
As a preferable technical scheme of the invention, the method for calculating the final positive angle alpha in the step S1 is to take the span length of the ith span as l i Taking the absolute value ordinate of the span end at the two ends of the ith span as H i And H i+1 Taking the final positive angle of the span as alpha i
There is a case where the number of the group,
wherein Δh i ＝H i -H i+1
Then there is theta' i ＝θ i -α i Wherein θ' i Is the final positive inclination angle of the ith span, theta i Is the measured tilt angle of the ith span.
As a preferable technical scheme of the invention, the method for constructing the deflection curve function of the bridge or the plate body is that the ith span is provided with k inclinometers, and the deflection curve of the ith span upper beam is y i (x)，y i (x) Meet the deflection boundary condition of the span, y i (x) The expression of (2) is as follows:
wherein x refers to an axial abscissa taking the left beam end of the span of the bridge or the plate body as an origin and taking the axis of the bridge or the plate body as a transverse positive axis; l is the span length of the span of the bridge or slab,is a constructed orthogonal polynomial basis function.
As a preferable technical scheme of the invention, the method for fitting the cross deflection curve function of the constructed bridge or plate body by the least square method of the orthogonal polynomial basis function is to construct the orthogonal polynomial basis function and select the knownAnd->Can get the inclusion->A set of orthogonal functions, including +.>Is of a structure ofA first order function expression of an orthogonal polynomial basis function,
wherein a and b are coefficients in the construction process, x is an axial abscissa taking the left beam end of the span of the bridge or the plate body as an origin and the axis of the bridge or the plate body as a transverse positive axis,
thereby obtaining k mutually orthogonal functionsSubstituting the coefficient matrix A, sorting the expression to obtain,
substituting A into A T AX * ＝A T θ', get the approximate solution of equation X * Wherein X is * ＝(X 1 ，X 2 ，...，X k ) T ，θ’＝(θ' 1 ，θ’ 2 ，...，θ’ k ) T For the final tilt angle after final correction,
x is to be * ＝(X 1 ，X 2 ，...，X k ) T Substituted into
Obtaining a preliminary deflection curve function of the whole bridge or the plate body.
As a preferable technical scheme of the invention, the method for settling and correcting the preliminary deflection curve function of the whole bridge or the plate body in the step S5 is that,
then y' i (x) The x in the formula refers to an axial abscissa taking the left beam end in the span of the bridge or the plate body as an origin and taking the axis of the bridge or the plate body as a transverse positive axis as a deflection curve function of the whole bridge or the plate body; l is the span length of the span of the bridge or slab.
As a preferred technical solution of the present invention,
the beneficial effects of the invention are as follows: according to the beam and plate vertical displacement calculation method based on the corner, firstly, the span length l of each span of a bridge or a plate body, the actual measurement inclination angle theta of each span and the absolute value ordinate H of the span ends of two ends of each span are measured and calculated to obtain a final positive angle alpha; final correction is carried out on the inclination angles theta of the m spans by using the final positive angle alpha to obtain a final positive inclination angle theta'; constructing a cross-deflection curve function of the bridge or the plate body; constructing an orthogonal polynomial basis function, and fitting a cross deflection curve function of the constructed bridge or plate body by using a least square method of the orthogonal polynomial basis function to obtain a preliminary deflection curve function of the whole bridge or plate body; and carrying out sedimentation final correction on the preliminary deflection curve function of the whole bridge or the plate body to obtain the final deflection curve function of the whole bridge or the plate body. The method is used for calculating the deflection (longitudinal plane displacement value of connecting lines of two opposite end points of each point in each span) displacement values of each point of the steel structure, the concrete structure plate body and the beam body in deflection change of the steel structure, the concrete structure plate body and the beam body, and obtaining absolute settlement of the steel structure, the concrete structure plate body and the beam body end points by increasing monitoring of the steel structure, the concrete structure plate body and the beam body end points to obtain the longitudinal plane displacement values of each point, so that the obtained longitudinal plane displacement values are more accurate and have smaller errors.
Drawings
The accompanying drawings are included to provide a further understanding of the invention and are incorporated in and constitute a part of this specification, illustrate the invention and together with the embodiments of the invention, serve to explain the invention. In the drawings:
FIG. 1 is a flow chart of a method for calculating vertical displacement of beams and plates based on rotation angles.
Detailed Description
The preferred embodiments of the present invention will be described below with reference to the accompanying drawings, it being understood that the preferred embodiments described herein are for illustration and explanation of the present invention only, and are not intended to limit the present invention.
Examples: as shown in FIG. 1, the method for calculating the vertical displacement of the beam and the plate based on the corner comprises the following steps:
step S1: measuring to obtain the span length l of each span of the bridge or the plate body, the actually measured inclination angle theta of each span and the absolute value ordinate H of the span ends of the two ends of each span, and calculating to obtain a final positive angle alpha;
step S2: final correction is carried out on the inclination angles theta of the m spans by using the final positive angle alpha, so as to obtain a final positive inclination angle theta' after final correction;
step S3: constructing a cross-deflection curve function of the bridge or the plate body;
step S4: constructing an orthogonal polynomial basis function, and fitting a cross deflection curve function of the constructed bridge or plate body by using a least square method of the orthogonal polynomial basis function to obtain a preliminary deflection curve function of the whole bridge or plate body;
step S5: and carrying out sedimentation final correction on the preliminary deflection curve function of the whole bridge or the plate body to obtain the final deflection curve function of the whole bridge or the plate body.
Wherein, the method for calculating the final positive angle alpha in the step S1 is to take the span length of the ith span as l i Taking the absolute value ordinate of the span end at the two ends of the ith span as H i And H i+1 Taking the final positive angle of the span as alpha i
There is a case where the number of the group,
wherein Δh i ＝H i -H i+1
Then there is theta' i ＝θ i -α i Wherein θ' i Is the final positive inclination angle of the ith span, theta i Is the measured tilt angle of the ith span.
Wherein the structureThe method for constructing the deflection curve function of the bridge or the plate body is that the ith span is provided with k inclinometers, and the deflection curve of the ith span upper beam is y i (x)，y i (x) Meet the deflection boundary condition of the span, y i (x) The expression of (2) is as follows:
wherein x refers to an axial abscissa taking the left beam end of the span of the bridge or the plate body as an origin and taking the axis of the bridge or the plate body as a transverse positive axis; l is the span length of the span of the bridge or slab,is a constructed orthogonal polynomial basis function.
As a preferable technical scheme of the invention, the method for fitting the cross deflection curve function of the constructed bridge or plate body by the least square method of the orthogonal polynomial basis function is to construct the orthogonal polynomial basis function and select the knownAnd->Can get the inclusion->A set of orthogonal functions, including +.>As a first order function expression of the constructed orthogonal polynomial basis function,
wherein a and b are coefficients in the construction process, x is an axial abscissa taking the left beam end of the span of the bridge or the plate body as an origin and the axis of the bridge or the plate body as a transverse positive axis,
thereby obtaining k mutually orthogonal functionsSubstituting the coefficient matrix A, sorting the expression to obtain,
substituting A into A T AX * ＝A T θ', get the approximate solution of equation X * Wherein X is * ＝(X 1 ，X 2 ，…，X k ) T ，θ'＝(θ' 1 ，θ' 2 ，…，θ' k ) T For the final tilt angle after final correction,
x is to be * ＝(X 1 ，X 2 ，…，X k ) T Substituted into
Obtaining a preliminary deflection curve function of the whole bridge or the plate body.
The method for settling and correcting the preliminary deflection curve function of the whole bridge or the plate body in the step S5 is that,
then y' i (x) The x in the formula refers to an axial abscissa taking the left beam end in the span of the bridge or the plate body as an origin and taking the axis of the bridge or the plate body as a transverse positive axis as a deflection curve function of the whole bridge or the plate body; l is the span length of the span of the bridge or slab.
According to the beam and plate vertical displacement calculation method based on the corner, firstly, the span length l of each span of a bridge or a plate body, the actual measurement inclination angle theta of each span and the absolute value ordinate H of the span ends of two ends of each span are measured and calculated to obtain a final positive angle alpha; final correction is carried out on the inclination angles theta of the m spans by using the final positive angle alpha to obtain a final positive inclination angle theta'; constructing a cross-deflection curve function of the bridge or the plate body; constructing an orthogonal polynomial basis function, and fitting a cross deflection curve function of the constructed bridge or plate body by using a least square method of the orthogonal polynomial basis function to obtain a preliminary deflection curve function of the whole bridge or plate body; and carrying out sedimentation final correction on the preliminary deflection curve function of the whole bridge or the plate body to obtain the final deflection curve function of the whole bridge or the plate body. The method is used for calculating the deflection (longitudinal plane displacement value of connecting lines of two opposite end points of each point in each span) displacement values of each point of the steel structure, the concrete structure plate body and the beam body in deflection change of the steel structure, the concrete structure plate body and the beam body, and obtaining absolute settlement of the steel structure, the concrete structure plate body and the beam body end points by increasing monitoring of the steel structure, the concrete structure plate body and the beam body end points to obtain the longitudinal plane displacement values of each point, so that the obtained longitudinal plane displacement values are more accurate and have smaller errors.
Finally, it should be noted that: the foregoing description is only a preferred embodiment of the present invention, and the present invention is not limited thereto, but it is to be understood that modifications and equivalents of some of the technical features described in the foregoing embodiments may be made by those skilled in the art, although the present invention has been described in detail with reference to the foregoing embodiments. Any modification, equivalent replacement, improvement, etc. made within the spirit and principle of the present invention should be included in the protection scope of the present invention.
Claims (1)
1. The method for calculating the vertical displacement of the beam and the plate based on the corner is characterized by comprising the following steps of:
step S1: measuring to obtain the span length l of each span of the bridge or the plate body, the actually measured inclination angle theta of each span and the absolute value ordinate H of the span ends of the two ends of each span, and calculating to obtain a final positive angle alpha;
step S2: final correction is carried out on the inclination angles theta of the m spans by using the final positive angle alpha, so as to obtain a final positive inclination angle theta' after final correction;
the method for calculating the final positive angle alpha in the step S1 is that the span length of the ith span is l i Taking the absolute value ordinate of the span end at the two ends of the ith span as H i And H i+1 Taking the final positive angle of the span as alpha i ，
There is a case where the number of the group,
wherein Δh i ＝H i -H i+1
Then there is theta' i ＝θ i -α i Wherein θ' i Is the final positive inclination angle of the ith span, theta i The measured inclination angle of the ith span;
step S3: constructing a cross-deflection curve function of the bridge or the plate body;
the method for constructing the deflection curve function of the bridge or the plate body is that the ith span is provided with k inclinometers, and the deflection curve of the ith span upper beam is y i (x)，y i (x) Meet the deflection boundary condition of the span, y i (x) The expression of (2) is as follows:
wherein x refers to an axial abscissa taking the left beam end of the span of the bridge or the plate body as an origin and taking the axis of the bridge or the plate body as a transverse positive axis; l is the span length of the span of the bridge or slab,is a constructed orthogonal polynomial basis function;
step S4: constructing an orthogonal polynomial basis function, and fitting a cross deflection curve function of the constructed bridge or plate body by using a least square method of the orthogonal polynomial basis function to obtain a preliminary whole bridgeA deflection curve function of the beam bridge or the plate body; the method for fitting the cross deflection curve function of the bridge or the plate body by the least square method of the orthogonal polynomial basis function comprises the steps of constructing the orthogonal polynomial basis function and selecting a known oneAnd->Can get the inclusion->A set of orthogonal functions, including +.>As a first order function expression of the constructed orthogonal polynomial basis function,
wherein a and b are coefficients in the construction process, x is an axial abscissa taking the left beam end of the span of the bridge or the plate body as an origin and the axis of the bridge or the plate body as a transverse positive axis,
thereby obtaining k mutually orthogonal functionsSubstituting the coefficient matrix A, sorting the expression to obtain,
substituting A into Cramer matrix A T AX * ＝A T θ', get the approximate solution of equation X * Wherein X is * ＝(X 1 ，X 2 ，...，X k ) T ，θ’＝(θ 1 ’，θ 2 ’，...，θ’ k ) T For the final tilt angle after final correction,
x is to be * ＝(X 1 ，X 2 ，...，X k ) T Substituted into
Obtaining a preliminary deflection curve function of the whole bridge or the plate body;
step S5: settling and correcting the preliminary deflection curve function of the whole bridge or the plate body to obtain a final deflection curve function of the whole bridge or the plate body;
the method for settling and correcting the preliminary deflection curve function of the whole bridge or the plate body in the step S5 is that,
Δh i ＝H i -H i+1 ，
then y' i (x) The x in the formula refers to an axial abscissa taking the left beam end in the span of the bridge or the plate body as an origin and taking the axis of the bridge or the plate body as a transverse positive axis as a deflection curve function of the whole bridge or the plate body; l is the span length of the span of the bridge or slab.
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